Question

K is the midpoint of JL • JK = 6x and KL = 3x + 3. Find JK, KL, and JL.

Answer 1

If K is the midpoint of JL, then the segment that goes from J to K (JK) is equal in length to the the segment that goes from K to L (KL).

Then, we can write:

`\begin{gathered} JK=KL \\ 6x=3x+3 \\ 6x-3x=3 \\ 3x=3 \\ x=(3)/(3) \\ x=1 \end{gathered}`

With the value of x we can find the values of the segments:

`\begin{gathered} JK=6x=6\cdot1=6 \\ KL=3x+3=3\cdot1+3=3+3=6\text{ (we already know that JK=KL)} \\ JL=JK+KL=2\cdot JK=2\cdot6=12\text{ (two times the half segment JK)} \end{gathered}`

Answer:

JK = 6

KL = 6

JL = 12